Bumgarner worked the count to 3-2 before sending the seventh pitch of the at-bat into the left-field seats.
"I fouled the previous pitch off my knee," Bumgarner said. "So I just tried to stay inside [the next one] a little more and was able to make the adjustment and hit it pretty good."
The home run was Bumgarner's third of the season and the ninth of his career. No other pitcher in baseball has more than one home run this year.
The left-hander became the first opposing pitcher to go deep against the Athletics since the Orioles' Dave McNally homered off Ken Holtzman in 1972, one year before the American League adopted the designated hitter position.
"He won the silver bat last year for a reason," Giants manager Bruce Bochy said, referring to Bumgarner being named the top hitter at his position in 2014. "It just goes to show you how pitchers can help themselves besides just throwing the ball."
Duffy added that having Bumgarner manning the final spot in the batting order can completely change how opposing pitchers strategically maneuver through San Francisco's lineup.
"When he's in, we're one through nine a tough out," Duffy said.
In 43 at-bats this season, Bumgarner is making a case to take home back-to-back Silver Slugger Awards. He has more home runs than full-time players Angel Pagan and Nori Aoki and as many long balls as part-timers Andrew Susac and Gregor Blanco.
"He's a strong kid," Duffy said. "When he connects, it's going to be hit hard."
The 2014 World Series Most Valuable Player is proving he can help the Giants win in more ways than one. Even on a day where he didn't have his best stuff, Bumgarner allowed just one run in seven innings and made up for it with his solo blast.